在 Pytorch 中估计高斯模型的混合

我实际上想估计一个以高斯混合作为基本分布的归一化流，所以我有点被火炬困住了。但是，您可以通过估计 torch 中高斯模型的混合来在代码中重现我的错误。我的代码如下：

import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

import torch
from torch import nn
from torch import optim
import torch.distributions as D

num_layers = 8
weights = torch.ones(8,requires_grad=True).to(device)
means = torch.tensor(np.random.randn(8,2),requires_grad=True).to(device)#torch.randn(8,2,requires_grad=True).to(device)
stdevs = torch.tensor(np.abs(np.random.randn(8,2)),requires_grad=True).to(device)
mix = D.Categorical(weights)
comp = D.Independent(D.Normal(means,stdevs), 1)
gmm = D.MixtureSameFamily(mix, comp)

num_iter = 10001#30001
num_iter2 = 200001
loss_max1 = 100
for i in range(num_iter):
    x = torch.randn(5000,2)#this can be an arbitrary x samples
    loss2 = -gmm.log_prob(x).mean()#-densityflow.log_prob(inputs=x).mean()
    optimizer1.zero_grad()
    loss2.backward()
    optimizer1.step()

我得到的错误是：

0
8.089411823514835
Traceback (most recent call last):

  File "/home/cameron/AnacondaProjects/gmm.py", line 183, in <module>
    loss2.backward()

  File "/home/cameron/anaconda3/envs/torch/lib/python3.7/site-packages/torch/tensor.py", line 221, in backward
    torch.autograd.backward(self, gradient, retain_graph, create_graph)

  File "/home/cameron/anaconda3/envs/torch/lib/python3.7/site-packages/torch/autograd/__init__.py", line 132, in backward
    allow_unreachable=True)  # allow_unreachable flag

RuntimeError: Trying to backward through the graph a second time, but the saved intermediate results have already been freed. Specify retain_graph=True when calling backward the first time.

正如您所看到的，模型运行了 1 次迭代后。

您的代码中存在排序问题，因为您在训练循环之外创建高斯混合模型，那么在计算损失时，高斯混合模型将尝试使用您在定义模型时设置的参数的初始值，但是optimizer1.step()已经修改了该值，所以即使您设置了loss2.backward(retain_graph=True)还是会出现这样的错误：RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation

解决这个问题的方法很简单，只要更新参数就创建新的高斯混合模型，示例代码按预期运行：

import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

import torch
from torch import nn
from torch import optim
import torch.distributions as D

num_layers = 8
weights = torch.ones(8,requires_grad=True)
means = torch.tensor(np.random.randn(8,2),requires_grad=True)
stdevs = torch.tensor(np.abs(np.random.randn(8,2)),requires_grad=True)

parameters = [weights, means, stdevs]
optimizer1 = optim.SGD(parameters, lr=0.001, momentum=0.9)

num_iter = 10001
for i in range(num_iter):
    mix = D.Categorical(weights)
    comp = D.Independent(D.Normal(means,stdevs), 1)
    gmm = D.MixtureSameFamily(mix, comp)

    optimizer1.zero_grad()
    x = torch.randn(5000,2)#this can be an arbitrary x samples
    loss2 = -gmm.log_prob(x).mean()#-densityflow.log_prob(inputs=x).mean()
    loss2.backward()
    optimizer1.step()

    print(i, loss2)